Nematic Domains and Resistivity in an Itinerant Metamagnet Coupled to a Lattice

The nature of the emergent phase near a putative quantum critical point in the bilayer ruthenate ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ has been a recent subject of intensive research. It has been suggested that this phase may possess electronic nematic order (ENO). In this work, we investigate the possibility of nematic domain formation in the emergent phase, using a phenomenological model of electrons with ENO and its coupling to lattice degrees of freedom. The resistivity due to the scattering off the domain walls is shown to closely follow the ENO parameter. Our results provide qualitative explanations for the dependence of the resistivity on external magnetic fields in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$.

Figure 1

Normal modes.

Figure 2

The red, blue, and green represent the negative, positive, and zero ENO parameter, respectively. Here, $A_1=20$, $A_2=20$, $A_3=0.001$, $B=1$, $C_3=100$, $t=0.1$, $t^{\prime }=0$, $F=0.2$, and $g=0.2$. The electron filling is $\frac{120}{256}$ per site to be slightly away from the van Hove singularity.

Figure 3

$\kappa$ as a function of (a) the electron-lattice coupling and (b) the anharmonicity. We use $t^{\prime }=0$, $F=2t$, and $B=20t$. ${\overline{C}}_3=0.05$ for (a) and $\overline{g}=0.1$ for (b).

Figure 4

The dashed line denotes the uniform ENO parameter in the mean-field theory [12]. The solid lines represent the resistivity with $t^{\prime }=0$, and $0.4t$. Here we use $\rho /\rho (Q=0)=\frac{\alpha }{\alpha -Q(0{)}^2}$ with $\alpha =0.24$ and $F=1.974t$.